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Archy [21]
3 years ago
9

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 50.2 × 105 kg, of

which 12.5 × 105 kg is fuel. The rocket engine is then fired for 450 s, during which fuel is consumed at the rate of 370 kg/s. The speed of the exhaust products relative to the rocket is 4.90 km/s. (a) What is the rocket's thrust? After the 450 s firing, what are (b) the mass and (c) the speed of the rocket?
Physics
1 answer:
AysviL [449]3 years ago
6 0

Answer:

165.2762 m/sec

Explanation:

The initial mass of the rocket and the fuel

M₀ = 5.02e6 kg

The initial mass of the fuel

Mf₀ = 1.25e6 kg

The rate of fuel consumption

dm/dt = 370 kg/sec

The duration of the rocket burn

Δt = 450 sec

The rocket exhaust speed

Ve = 4900 m/sec

The thrust, T

T = Ve (dm/dt) = 1813000 kg m/sec²

The mass of the expended propellant, ΔM

ΔM = Δt (dm/dt) = 166500 kg

The rocket's mass after the burn

M₁ = M₀ − ΔM = 4853500 kg

The speed of the rocket after the burn

Δv = Ve ln(M₀/M₁) = 165.2762 m/sec

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Answer:

See the explanation below

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3 years ago
Time dilation: A missile moves with speed 6.5-10 m/s with respect to an observer on the ground. How long will it take the missil
tatyana61 [14]

Answer:

The time taken by missile's clock is 4.6\times 10^{6} s

Solution:

As per the question:

Speed of the missile, v_{m = 6.5\times 10^{3}} m/s

Now,

If 'T' be the time of the frame at rest then the dilated time as per the question is given as:

T' = T + 1

Now, using the time dilation eqn:

T' = \frac{T}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}

\frac{T'}{T} = \frac{1}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}

\frac{T + 1}{T} = \frac{1}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}

1 + \frac{1}{T} = \frac{1}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}

1 + \frac{1}{T} = (1 + (\frac{v_{m}}{c})^{2})^{- \frac{1}{2}}         (1)

Using binomial theorem in the above eqn:

We know that:

(1 + x)^{a} = 1 + ax

Thus eqn (1) becomes:

1 + \frac{1}{T} = 1 - \frac{- 1}{2}.\frac{v_{m}^{2}}{c^{2}}

T = \frac{2c^{2}}{v_{m}^{2}}

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T = \frac{2(3\times 10^{8})^{2}}{(6.5\times 10^{3})^{2}}

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4 0
3 years ago
A chicken crosses a 7.50 m wide road at a constant speed of 0.367 m/s. How much time does it take to cross (in seconds)?
mars1129 [50]
<h3><u>Answer;</u></h3>

= 20.436 seconds

<h3><u>Explanation;</u></h3>

Speed = Distance × time

Therefore;

Time = Distance/speed

Distance = 7.50 m, speed = 0.367 m/s

Time = 7.50/0.367

         <u>= 20.436 seconds </u>

7 0
3 years ago
Read 2 more answers
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